How to fix "Select Non Manifold" Errors
I believe that's not an error, it's doing what you're exactly asking it to do. 
Joining meshes using Ctrl + J do not affect their geometry, it just puts them as one object, think of it as a way of grouping meshes, any doubles or holes will remain the same, so what you actually did is overlapping your meshes, what you need to do is to close the holes, remove doubles, in other words make the mesh manifold. Trying to understand better what a manifold mesh is, think about it as a model of an open bottle, with a single surface, the hole at the top makes it non manifold, since the "exposed" inside of the bottle,  has no dedicated faces, faces normals are pointing outside, while adding a Solidify modifier, or closing the hole, makes it manifold (in case there are no doubles) because all "exposed" faces now have normals pointing outside the volume of the mesh itself.